Problem with Texture on Plane
There is a much easier way to project an image onto a plane.


Enable the images as planes addon under 'user preferences'
Press 'SHIFT + A' -> Mesh -> Images as planes

Then search for your image and voila!


This does not really answer your question but it should work out fine for you I guess.

If you really need to fix the problem you're facing:


Get into 'edit mode'
Select all (press 'A')
Go to top view in ortographic projection
Press 'U'
select 'project from view'
Go to image editor en scale your UV's if necessary
Done!


If you still have problems after these steps, try recalculating the normals.
(shortcut: 'CTR +N')